It's utter nonsense; there are no facts to support it.

I have an earlier answer explaining how we know the current year is [2020]. I discuss the phantom time bit at the end.

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Dionysius Exiguus came up with the modern world's most-used system for numbering years (Anno Domini, sometimes rebranded Common Era) in the early sixth century. For hundreds of years, however, the few Europeans dating documents preferred to continue the traditional system of dating by regnal year.

By the high Middle Ages, chroniclers like Herman of Reichanau are numbering their entries by A.D. year, but we're still not quite at the point where they're common usage in charters or in people's minds. (Court testimony from even the late Middle Ages sometimes has people figure dates from either kings' regnal year or with reference to more local events).

Just to make things even more interesting, Hebrew calendar years are also a creation of the High Middle Ages.

And yet, in these 4-5 centuries of only scattershot use of the A.D. system, there are isolated instances of writers who do pick it up and run with it. Bede in 7th-8th century England is perhaps the most famous. How did they do it? Easter!

The Christian liturgical calendar(s) involves some feasts that are fixed to a date and others that are more fluid. Most importantly and controversially, Easter, the history (and present, see: Catholic versus Orthodox) of whose dating is a giant mess. The early Church decided on a date for Easter that relates to the vernal equinox.

But here's the thing. As you know, and as ancient people knew, years are not actually 365 days. Hence the introduction of leap years. And the presence of leap years (in the Julian calendar, which has too many leap years and so would be a problem by the sixteenth century) combined with the decision that Easter must always be a Sunday meant that the date of Easter had to be calculated. Indeed, this computus was a crucial duty of the early medieval clergy. They made table after table that calculated and listed the dates of Easter for centuries to come.

So even across centuries of sporadic functional use of AD/CE, the medieval Church placed an absolutely premium on keeping track of the advancement of years in terms fixed to the date once presumed to be either the conception or birth of Christ.

There are some conspiracy theories floating around about "phantom time" that jump off from just that lack of consistent functional use of AD dating in Western Christian sources. These fall apart on a couple of grounds. First, the Hijri or Islamic calendar was in use from the mid-7th century, and we can compare its advancement of years to the European.

Should one posit a transnational conspiracy to erase or add centuries, let the stars be your guide. It is possible to date significant astronomical events, such as things retro-identified as comets with known visiting patterns or eclipses. The dating of these phenomena in ancient and medieval sources line up with what we would calculate if today were 2020 AD/CE--which it is.